Question

求极限lim(n→∝)(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^2n)

不会整合这个式子

Answer 1

解，A=(1+1/2)(1+1/2^2)，，，(1+1/2^2n)
=2(1-1/2)(1+1/2)(1+1/2^2)，，，(1+1/2^2n)
=2(1-1/2^4n)
则n→00，则A=2

Answer 2

（1+1/2）(1+1/2^2)(1+1/2^4)...(1+1/2^2n)=2(1-1/2)（1+1/2）(1+1/2^2)(1+1/2^4)...(1+1/2^2n)
=2(1-1/2^2)(1+1/2^2)(1+1/2^4)...(1+1/2^2n)
=2(1-1/2^4n)
lim(n→正无穷)（1+1/2）(1+1/2^2)(1+1/2^4)...(1+1/2^2n)
lim(n→正无穷)2(1-1/2^4n)=2